Free public university:
Heh? Where are free public universities? I'm have to assume that you are not talking about US universities.
But even if they are free, why shouldn't an author be allowed to choose?
In all cases, I think the author should be allowed to choose.
The professors working at the tax funded(Nothing is free afterall) universities in some european countries have their salaries paid for by the tax payers, thus it is quite reasonable that their work should belong to the public.
Students who aren't getting paid to create the projects should own the rights to their work in all cases and private schools should, just like any other company own the work of its staff.
If private universities get partial public funding it might make sense to sort out some arrangement where copyright is transfered to the public after X years (depending on how much of the work is paid for by the public)